The legs of a right triangle are 6 and 8 cm. Find the hypothesis and the area of the triangle.

1) The hypotenuse can be calculated by the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the legs:
x ^ 2 = 6 ^ 2 + 8 ^ 2;
x ^ 2 = 36 + 64;
x ^ 2 = 100;
x = 10 cm.
2) The area of a right-angled triangle is equal to the product of the legs divided by two. We get: 6 * 8/2 = 24 cm2.
Answer: the hypotenuse is 10 cm, the area of the triangle is 24 cm2.